Speaking via video link in the latest address to a European parliament, Mr Zelensky said Russia wanted to break through into the rest of Europe.
He said: "For Russian troops, Ukraine is the gates of Europe, where they want to break in, but barbarism must not be allowed to pass.”
His statement came as the UK Government blamed Vladimir Putin's Kremlin for a video clip in which imposters speak to three Cabinet ministers.
The Ministry of Defence (MoD) described the videos as "doctored clips" from the "Russian state" and issued warnings against believing their contents. However, officials seem to be struggling to get the clips removed from YouTube.
In the second video, released on Tuesday, Mr Wallace seemingly suggests to the caller, who he believed was Ukrainian prime minister Denys Shmyhal, the UK is "running out of our own" NLAW anti-tank weapons.
The MoD said Britain has provided more than 4,000 NLAWs to Ukraine's forces, but still had "enough weapons systems to defend both UK national security and maintain our commitments" to Nato.
"This video, like most Russian propaganda, is fed out to obscure and manipulate the truth," the statement said.
"People should be very sceptical about reporting on, and accepting as real, any part of these Russian state doctored clips."
In his address to the Italian parliament, Mr Zelensky urged politicians to sanction Russian oligarchs.
He said: “You know very well who orders troops to go to war and who propagates this. Almost all of them use Italy as a place to rest. Do not be a resort for murderers.
"Freeze all their property, accounts and yachts. Freeze all the assets of those who have influence, let them use it for peace. Support sanctions against Russia, a full trade embargo, starting with oil."
He also asked Italy to ban Russian ships from entering Italian ports and sanction all Russian banks.
"This war must end as soon as possible,” he said. “Restore peace. Remove enemy troops from Ukraine. Carry out de-mining – and reconstruction. Reconstruction of Ukraine after this war. Together with you, together with Italy. Together with Europe. Together – in the European Union."
Italian PM Mario Draghi said his country wanted to see Ukraine in the EU, and that it must offer military aid to the country to halt massacres.
Mr Zelensky told Ukrainian television late on Monday that he would be prepared to consider waiving any bid by Ukraine to join Nato – key Russian demand – in exchange for a ceasefire, the withdrawal of Russian troops and a guarantee of Ukraine's security.
The Ukrainian president also suggested Kyiv would be open to future discussions on the status of Crimea, which Russia seized in 2014, and areas of the eastern Donbas region held by Russian-backed separatists. But he said that was a topic for another time.
Russia’s assault on Ukraine has continued. However, Ukrainian forces said they had retaken a strategically important suburb of Kyiv, as Russian forces squeezed other areas near the capital and their attack on the southern port of Mariupol raged on.
Explosions and bursts of gunfire shook Kyiv and black smoke rose from a spot in the north. Intensified artillery fire could be heard from the north-west, where Russia has sought to encircle and capture several suburban areas of the capital – a crucial target.
Residents sheltered at home or underground under a 35-hour curfew imposed by authorities in the capital that runs to Wednesday morning.
Early on Tuesday, Ukrainian troops forced Russian forces out of the Kyiv suburb of Makariv after a fierce battle, Ukraine's defence ministry said.
The regained territory allowed Ukrainian forces to retake control of a key highway and block Russian troops from surrounding Kyiv from the north-west.
Still, the Ukrainian defence ministry said Russian forces battling toward Kyiv were able to partially take other the north-western suburbs Bucha, Hostomel and Irpin, some of which had been under attack since Russia's military invaded almost a month ago.
Russian forces also pressed their siege of Mariupol after the southern port city's defenders refused demands to surrender, with fleeing civilians describing relentless bombardments and corpses lying in the streets.
Mariupol officials said on March 15 that at least 2,300 people had died in the siege, with some buried in mass graves. There has been no official estimate since then, but the number is feared to be far higher.
Those who have made it out of Mariupol told of a devastated city.
"There are no buildings there anymore," said 77-year-old Maria Fiodorova, who crossed the border to Poland on Monday after five days of travel.
The World Health Organisation (WHO) said it has verified 62 separate attacks on healthcare facilities in Ukraine since Russia's invasion began almost four weeks ago.
The organisation said 15 people had died in the attacks and at least 37 others had been injured.
Meanwhile, WHO officials in Poland say a rapid assessment suggests about half a million refugees who have arrived there are suffering from mental health problems, primarily due to trauma.
Figures suggest a total of 3.557 million people have fled Ukraine. The UK Home Office said on Tuesday that some 12,400 visas have been issued under the Ukraine family scheme. A total of 32,500 applications have been submitted so far, according to provisional data published on the department's website.